A mathematical model of marine mucilage, the case of the liga on the Basque coast

TL;DR

This paper develops a mathematical model to understand marine mucilage formation caused by diatoms under nutrient constraints, analyzing its properties and exploring parameter identification through numerical experiments.

Contribution

It introduces a novel mathematical model for marine mucilage formation and analyzes its theoretical properties and potential for parameter estimation.

Findings

Model is well-posed and differentiable with respect to parameters

Numerical experiments demonstrate feasibility of parameter identification

Provides insights into biological mechanisms of mucilage formation

Abstract

In this paper we are interested in modeling the production of mucus by diatoms under the constraint of a nutrient limitation. The initial questioning comes from the observation of the so-called ''liga'' on the Aquitaine coast. The biological origin of the phenomenon is presented and discussed based on the existing litterature.A mathematical model is proposed and its theoretical properties are analized: well-posedness and differentiability with respect to the model parameters.Finally, numerical experiments are provided, investigating the possibility of parameter identification for the model using chemostat-type experiments.